Wikipedia:Featured article candidates/Euclidean algorithm/archive1: Difference between revisions
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**<s>"''r''<sub>''k''</sub> ≡ ''r''<sub>''k''−2</sub> mod ''r''<sub>''k''−1</sub>" Is there some article to which we can link '≡'? I'm not sure I know what it means.</s>
**:It means "equivalent to" in [[modular arithmetic]]. I'll make a link. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:58, 5 May 2009 (UTC)
**<s>I don't think the ''implementations'' section belongs in this article. [[WP:NOT|Wikipedia is not]] a how-to guide, and this section does not contain any new relevant information.</s>
**::Your initial reaction is similar to mine. Bu let me argue that the implementations contribute at least epsilon to the article for most readers, and for some readers may convey the algorithm's idea better than anything else. I note that [http://en.wikipedia.org/w/index.php?title=Euclidean_algorithm&oldid=276556143 when I arrived] at this article — then rated at nearly GA level by the Math WikiProject — the implementations were the article's main content, having been debated and perfected for over [http://en.wikipedia.org/w/index.php?title=Euclidean_algorithm&oldid=250714 seven years]. Some editors champion the pseudocode as the only valid way of defining the algorithm precisely. In deference to these editors and in deference to the many readers like them, I feel we should retain the Implementations section. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:18, 9 May 2009 (UTC)
**:::Deference to these editors? Pfft. Perhaps you have forgotten the disclaimer: "If you don't want your writing to be '''edited mercilessly''' or redistributed for profit by others, do not submit it." As for the readers, they come here for a lot of things that they really shouldn't (medical advice comes to mind). The very most we can do in regards to instruction content like this is to provide an informative link — perhaps to a WikiHow article or a programming site. I realize that you have the best intentions by wanting to keep the material, but the fact of the matter is that it really doesn't belong here. The other points you've brought up are largely irrelevant. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 03:32, 9 May 2009 (UTC)
**::Let me clarify the question with a triple negative. ;) I'm NOT saying that we should violate WP:NOT in order to NOT hurt the feelings of some devoted editors. Rather, the pivotal issue is whether the Implementations section allows us to ''explain the algorithm'' to readers who might not really understand it otherwise. I argue yes. It's not about providing snippets of HOWTO code, but rather providing another avenue that connects the algorithm to our readers. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 04:13, 10 May 2009 (UTC)
**:::You will not be able to find a pseudocode representation that all programmers will be able to understand. I am very experienced with TI-BASIC and I've twiddled with C++, but I'm not familiar with some of the notation you've used. As I see it, you have three options: Give whatever programming language you choose [[WP:UNDUE]] weight by explaining all of the relevant syntax, leave it vague and hope for the best, or remove the section altogether. I think at this point it's clear which option I'd prefer. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 03:32, 11 May 2009 (UTC)
**<s>"if the resulting negative remainder is smaller in absolute value than the typical positive remainder" You used "magnitude" earlier. I recommend swapping out "absolute value" for "magnitude" for consistency.</s>
**::OK, sounds good. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:18, 9 May 2009 (UTC)
**<s>"to the greatest length g that measures a and b evenly" The word "measures" seems a bit off. Shouldn't it be "divides"?</s>
**::A geometric length is qualitatively different than an integer. "Measure" or "measure off" is the standard vocabulary used for the former. The ancient Greeks distinguished the two operations (division and "measuring off"), and their concepts have carried over. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:18, 9 May 2009 (UTC)
**<s>"in other words, the lengths a and b are both multiples of the length g" I suggest the injection of the word "integer" before "multiples", without it, the whole concept is meaningless.</s>
**::Great catch, although I predict that most non-mathematicians would assume that "multiple = integer multiple". [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:18, 9 May 2009 (UTC)
**:::Aye,
**"The algorithm was likely known by Eudoxus of Cnidus (about 375 BC). The use of the technical term ἀνθυφαίρεσις (anthyphairesis, reciprocal subtraction) in Euclid and Aristotle (Topics IV) suggests that the algorithm predates Eudoxus." I see what you're getting at, but to some readers, these sentences may seem to contradict each other. Suggested rewrite: "The use of the technical term ἀνθυφαίρεσις (anthyphairesis, reciprocal subtraction) in Euclid and Aristotle (Topics IV) suggests that what we now know as the Euclidean Algorithm may have predated [[Eudoxus of Cnidus]], a Greek mathematician who died in approximately 350 BC." or some such. Meh. That's not exactly perfect either. Give it some thought.
**::That's a good suggestion, and very helpful. I toyed with the wording beforehand, but I didn't come up with anything as good as yours. I've uploaded a third wording that may combine the best of our efforts. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 04:13, 10 May 2009 (UTC)
**:::Ah, much better! More direct than mine, too. I'm confused about the last bit, though: "use of the technical term ἀνθυφαίρεσις (''anthyphairesis'', reciprocal subtraction) in Euclid and Aristotle (''Topics'' IV)" Did Euclid and Aristotle collaborate on a book called "Topics IV"? What's going on here? --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 03:32, 11 May 2009 (UTC)
**<s>"Euclid's algorithm was re-invented both in India and in China" "re-invent" often implies that an existing concept was significantly improved. I think "independently developed" or "independently discovered" might serve better.</s>
**::Good idea, made additional minor changes in wording. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:35, 9 May 2009 (UTC)
**"the Indian mathematician and astronomer Aryabhata described the algorithm as the "pulverizer"" Erm... why?
**::Good question! The historical record does not say, as far as I can tell. One author speculates that it's because the algorithm "pulverizes" difficult linear Diophantine equations in only a few steps, emphasizing its power to solve problems. Its operation also vaguely resembles a pulverizer that breaks a large stone into medium-sized stones, then into small stones, and thence into dust. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:35, 9 May 2009 (UTC)
**:::Both of those certainly make sense. Whichever explanation best adheres to the available sources should probably be added to the article—I'm sure some readers will have the same question I did. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 03:32, 11 May 2009 (UTC)
**<s>"and applied it solving linear Diophantine equations" Consider changing "applied it solving" to "used it to solve".</s>
**::Much better, thank you! [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:35, 9 May 2009 (UTC)
**<s>"Although a special case of the Chinese remainder theorem was described earlier by Chinese mathematician and astronomer Sun Tzu" The use of "earlier" implies a relation to the previous sentence rather than the following clause. Suggest "was described earlier" to "had already been described".</s>
**::Good! [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:35, 9 May 2009 (UTC)
**<s>"The algorithm was first described in Europe in the second edition of Bachet's ''Problèmes plaisants et délectables'' (1624)." Which algorithm? The EA? Or the Chinese Remainder Theorem? Also, do you have a translation for that French title?</s>
**::Clarified EA, translated title. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:35, 9 May 2009 (UTC)
**"In the 19th century, Carl Friedrich Gauss used the Euclidean algorithm to demonstrate unique factorization of Gaussian integers by 1815 (published 1832), although he did not mention the algorithm in his earlier work, Disquisitiones Arithmeticae (1801), except as a method for continued fractions." If you include specific years, "In the 19th century" is redundant. Also, I'm confused by the 1815/1832 thing. Also, the second chunk is somewhat misleading. Suggested rewrite: "though he had mentioned the algorithm in his earlier work, Disquisitiones Arithmeticae (1801), simply as a method for solving continued fractions."
▲* More to come. Good work thus far. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 19:59, 3 May 2009 (UTC)
**"[[Dirichlet]] seems to have..." A person's full name (or at least their first name) should be given the first time they are mentioned.
**"would hold true for any other system of numbers in which the Euclidean algorithm could be applied" Should be "to which the", right?
**"Dirichlet's insight likely inspired Richard Dedekind to develop theories for new types of numbers, the algebraic integers, and more generally Euclidean domains." As this is written, it implies that Dedekind might or might not have developed those theories. Also, the ending construction implies that "new types of numbers, the algebraic integers, and more generally Euclidean domains" are all seperate items in a list, but my hunch is that the second is an example of the first. Suggested rewrite: "Richard Dedekind's theories for new types of numbers, such as algebraic integers and Euclidean domains, may have been inspired by Dirichlet's insight." If you do end up rewriting this sentence, be sure to tweak the following sentence to make sure it flows logically.
**"In 1829, Sturm showed..." Not sure why this chunk comes after the Dirichlet/Dedekind bit. I'm assuming that Dirichlet/Dedekind did their work after 1832, which may not be correct. If that is correct, then this section is somewhat out of order. If is not correct, then this is still out of order and specific years should be added for clarity (if possible).
--'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 19:59, 3 May 2009 (UTC)
:::Thank you very much for your careful reviewing! The article is definitely improving. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)
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